IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-0-85729-428-9_11.html
   My bibliography  Save this book chapter

Infinite Field Extensions

In: Basic Algebra

Author

Listed:
  • P. M. Cohn

    (University College London, Department of Mathematics)

Abstract

Chapter 7 was almost entirely devoted to field extensions of finite degree and concentrated on Galois theory . However, even an introductory account should make some mention of infinite field extensions, and we shall discuss them in the present chapter, including transcendental extensions (Section 11.3) and infinite Galois theory (Section 11.8). The notion of algebraic dependence has similarities to linear dependence, which are described in abstract form in Section 11.1 and applied in Section 11.2. In addition there are concise accounts of topics that are useful in commutative ring theory and algebraic geometry, besides being of independent interest : separability (Sections 11.4 and n .s), the interactions of two or more subfields (Sections 11.6 and 11.7), applications of Galois theory (Section 11.9) and abelian extensions of finite exponent (Section 11.10).

Suggested Citation

  • P. M. Cohn, 2003. "Infinite Field Extensions," Springer Books, in: Basic Algebra, chapter 11, pages 397-447, Springer.
    • Handle: RePEc:spr:sprchp:978-0-85729-428-9_11
    DOI: 10.1007/978-0-85729-428-9_11
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-0-85729-428-9_11. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.